Top Voted Answer

Bethesda made a nice point to still include the "Experience Progress Bar" in the loading screens at Level 20, showing a Level 21 at the end of the bar that you can't achieve. This, of course, fueled rumors that future DLC/expansions may raise the level cap.

Answers

Alas, no you cannot go beyond level 20if you want some inspiration, then go the alternative route if you were good go evil and vice versa. if that doesnt do it for you then take the time to actually explore a little bit, there are some easter eggs that you might have missed